Time-interleaving has long been recognized as an attractive technique for implementing analog-to-digital converter systems with very high sampling rates. However, to realize low distortion, the sample time skews between the different channels must be well matched. Since the channels' sample times will vary with temperature, supply voltage, and aging, it is desirable to monitor or estimate the timing skews during the normal operation of the system such that timing skew corrections can be made, as needed. While a number of simple timing skew estimation algorithms exist for two-channel time-interleaved analog-to-digital converter systems, the algorithms are not well suited for systems with more than two channels.
In a conventional time-interleaved multi-channel analog-to-digital converter system, a plurality of sub-analog-to-digital converters is operated in parallel, as shown in FIG. 1. As FIG. 1 illustrates, a conventional time-interleaved multi-channel analog-to-digital converter system includes multiple channels, four in this example (A, B, C, and D). Each channel includes a sub-analog-to-digital converter (32, 34, 36, and 38). Each sub-analog-to-digital converter (32, 34, 36, and 38) is connected to a clock and sequential selector circuit 10. The clock and sequential selector circuit 10 provide the clock signal for each sub-analog-to-digital converter (32, 34, 36, and 38) and the selection signal so that the appropriate channel is selected to produce the digital signal 40 for output from the time-interleaved multi-channel analog-to-digital converter system. Moreover, an analog signal, from an analog input 20, is input to each sub-analog-to-digital converter (32, 34, 36, and 38).
The conventional timing for the four channels shown in FIG. 1 is illustrated in FIG. 2. As illustrated in FIG. 2, the samples are assumed to be taken on the rising edge of the system clock and on the falling edge of the channel clocks (Clk-A, Clk-B, Clk-C, and Clk-D).
Based upon the illustrated sequence, if each sub-analog-to-digital converter (32, 34, 36, and 38) has a maximum sample rate of fc, the time-interleaved multi-channel analog-to-digital converter system can achieve a system sample rate of fs=M*fc, wherein M is the number of channels or number of sub-analog-to-digital converters.
As illustrated in FIG. 2, the conventional timing sequence utilizes a minimal length sequence for which the repeat rate of the timing pattern is equal to the number of elements in the array. Consequently, when M ADCs are used, the ADCs are used sequentially and the pattern repeats every M samples. When a minimal length sequence is used in a time-interleaved analog-to-digital converter, one may refer to such a system as a sequential time-interleaved analog-to-digital converter. Utilizing a minimal length sequence ensures that each ADC samples the input as soon as possible when the time-interleaved system is clocked at its maximum rate.
In such a time-interleaving system, the analog-to-digital converter system can achieve a very high sampling rate. However, to realize low distortion, the sub-analog-to-digital converters used in a time-interleaved system must be well matched. More specifically, to realize low distortion, it is important that the sample times of the sub-channels be equally spaced as shown in FIG. 2.
Deviations from the ideal spacing, often referred to as timing skews, lead to the generation of spurious tones. Spurious tones limit the spurious free dynamic range of the overall time-interleaved multi-channel analog-to-digital converter system. The frequency of the input signal, fi, and the magnitude of the timing skews, ΔT, limits the spurious free dynamic range. This relationship is governed by: SFDR=−20 log(2π(fi)(ΔT)) wherein SFDR is the spurious free dynamic range.
For example, if a system has a timing skew of one pico-second and an input signal of 250 MHz, the spurious free dynamic range will be limited to 56 dB. It is noted that the sample rate (fs) has no effect on the spurious free dynamic range.
Conventionally, spurious free dynamic range is improved by reducing the timing skews. To effectively reduce the timing skews, first the skews must be determined or estimated. Thereafter, the timing skews are corrected. Although, skews can be determined and corrected before using an analog-to-digital converter, this is undesirable because the timing skews may shift with time and with changes in operating conditions such as supply voltage and temperature.
Consequently, it is desirable to estimate and correct the timing skews while the analog-to-digital converter system is normally operating without the use of special calibration signals. For example, for a two-channel system, timing skews have been conventionally estimated and corrected during normal operations by correlation techniques and multipliers. These techniques are based on the use of two-channel timing skew estimation algorithms or more simply two-channel skew estimators. Although these conventional approaches are well suited for two-channel systems, the conventional approaches do not work well when extended to systems with more than two channels due to Nyquist limitations.
When M=2, the estimation techniques used to detect timing skews rely on mathematical operations on adjacent samples. In a two channel system, any pair of adjacent samples will be composed of one sample from the reference analog-to-digital converter and one sample from the slave analog-to-digital converter. Ideally, these samples are spaced 1/fs apart. One such algorithm estimates the timing skew by taking the difference between a sum of the magnitudes of the sum of the reference channel's sample and the following sample from the slave channel and a sum of the magnitudes of the sum of the slave channel's sample and the following sample from the reference channel. The sign of the estimate indicates the direction of the timing skew and the magnitude of the estimate is related to the magnitude of the timing skew.
When M>2, the spacing between the various channels is no longer 1/fs. For example, when M=4, the spacing between the reference channel and either a first channel or a third channel is 1/fs, and 3/fs, while the spacing between the reference channel and the second channel is 2/fs.
Since the spacing between the reference channel and any other channel is no longer approximately 1/fs, for the M>2 case, the common two channel skew estimators must be modified if they are to be applied to these systems.
There are two direct ways to modify the common two channel skew estimators. The first approach is to band-limit the system's input to only part of the system's full Nyquist zone. Such a solution would be applicable in some applications, but not all. The second approach is to use the components of the estimation to first determine which sub-band of the full Nyquist zone most of the energy lies. Then the appropriate sign of the estimate can be determined.
However, neither approach is well suited to broadband applications in which signal energy is approximately uniformly distributed over the Nyquist band.
An alternate approach to improving the spurious free dynamic range is to use channel randomization. When channel randomization is used, the sequence in which the channels are used is random or pseudo-random. However, channel randomization reduces the spurious tones by converting the spurious tones to noise. This additional noise can have a negative impact upon the output of the multi-channel system. If the mismatches in a system using channel randomization are significant, the resulting degradation in the noise, from the conversion of the spurious tones to noise, may be unacceptable. The solution to the degradation, as noted above, is to estimate and correct the timing skews.
Thus, it is desirable to find an alternate solution to the problem of extending timing skew estimation algorithms for two channel systems to the multi-channel case. This would enable the timing skews to be estimated and corrected during normal operations of a multi-channel system (more than two channels) to ensure acceptable matching and to obtain the desired level of performance.